On the Central Paths and Cauchy Trajectories in Semidefinite Programming

In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a … Read more

Interior Proximal Algorithm with Variable Metric for Second-Order Cone Programming: Applications to Structural Optimization and Support Vector Machines

In this work, we propose an inexact interior proximal type algorithm for solving convex second-order cone programs. This kind of problems consists of minimizing a convex function (possibly nonsmooth) over the intersection of an affine linear space with the Cartesian product of second-order cones. The proposed algorithm uses a distance variable metric, which is induced … Read more

A Filter Algorithm for Nonlinear Semidefinite Programming

This paper proposes a filter method for solving nonlinear semidefinite programming problems. Our method extends to this setting the filter SQP (sequential quadratic programming) algorithm, recently introduced for solving nonlinear programming problems, obtaining their respective global convergence results. Citation CMM-B-06/10 – 171 Centre for Mathematical Modelling, UMR 2071, Universidad de Chile-CNRS. Casilla 170-3 Santiago 3, … Read more

Perturbation analysis of second order programming problems

We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions. Citation Research Report 5293 (August … Read more